The origin of the ionization of the diffuse ionized gas in spirals - II. Modelling the distribution of ionizing radiation in NGC 157

In this paper we make a quantitative study of the hypothesis that the diffuse Halpha emitted from the discs of spiral galaxies owes its origin to the ionizing photons escaping from H II regions. The basis of the models is the assumption that a fraction of the Lyman continuum (Lyc) luminosity from the OB stars within each H II region escapes from the region, leaking into the diffuse gas. A basic input element of any such model is a position and luminosity catalogue in Halpha of the H II regions in the galaxy under examination, down to a low limiting luminosity, and we have previously produced a catalogue of this type for NGC 157. An initial family of models can then be generated in which the Lyc escaping from an H II region is parametrized in terms of the observed Halpha luminosity of the region and the escaping fluxes allowed through the diffuse disc gas. These models can then be refined using a measured map of Hi surface density to effect the down-conversion of the Lyc to Halpha. For NGC 157 an Hi map was available. Although its moderate angular resolution did limit the accuracy with which we could test our models, the predicted diffuse Halpha surface brightness distributions from our models were compared with the observed distributions showing that, in general terms, the hypothesis of density bounding for the H II regions allows us to predict well the spatial distribution of the diffuse ionized gas. In the model yielding the best fit to the data, the regions of lower luminosity lose a constant fraction of their ionizing flux to their surroundings, while for H II region luminosities above a specific transition value the ionizing escape fraction is a rising function of the Halpha luminosity.